Dynamic Shortest Paths Minimizing Travel Times and Costs

Ahuja, Ravindra K.; Orlin, James B.; Pallottino, Stefano; Scutellà, Maria Grazia

doi:10.2139/ssrn.344442

Cited by 28 publications

(37 citation statements)

References 12 publications

(4 reference statements)

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“…Algorithms based on the explicitly construction of the expanse graph have also been proposed, see the work of Ahuja et al (2003).…”

Section: State Of the Artmentioning

confidence: 99%

Solution approaches for determining user-oriented paths on dynamic networks

Pugliese

Guerriero

2015

IJSCIM

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This paper addresses the time dependent multi-objective constrained shortest path problem. Solving the problem aims at providing the user a Pareto-optimal solution associated with an efficient path. The solution process takes into account information given by the user in order to obtain a path, satisfying his/her requirements. For the first time, more than two criteria are considered and the reference point methodology is used to define the aggregation function. In addition, knapsack-like constraints are introduced in the formulation in order to model budget restrictions. Dynamic-programming-based algorithms are devised and tested on randomly generated networks and on real life instances derived from US city maps. The computational results underline that the proposed algorithms are able to solve the problem in a reasonable amount of time. This is a good result since the problem considered contains features of three NP-hard problems: the multi-objective, the constrained and the time dependent shortest path problems.

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“…Algorithms based on the explicitly construction of the expanse graph have also been proposed, see the work of Ahuja et al (2003).…”

Section: State Of the Artmentioning

confidence: 99%

Solution approaches for determining user-oriented paths on dynamic networks

Pugliese

Guerriero

2015

IJSCIM

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“…A number of algorithms in computer networks [22,8] also solve the problem of recomputing shortest path trees when edges are added to or removed from the graph. Some related work [6,3,19,4] for this problem proposes methods for exact computation of dynamic shortest paths in a variety of graph settings and in parallel or distributed scenarios. Our problem is however that of finding the maximum shortest path change between pairs of nodes, rather than that of designing incremental algorithms for maintaining shortest paths.…”

Section: Related Workmentioning

confidence: 99%

Finding Top-k Shortest Path Distance Changes in an Evolutionary Network

Gupta

Aggarwal²

2011

Advances in Spatial and Temporal Databases

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Abstract. Networks can be represented as evolutionary graphs in a variety of spatio-temporal applications. Changes in the nodes and edges over time may also result in corresponding changes in structural garph properties such as shortest path distances. In this paper, we study the problem of detecting the top-k most significant shortest-path distance changes between two snapshots of an evolving graph. While the problem is solvable with two applications of the all-pairs shortest path algorithm, such a solution would be extremely slow and impractical for very large graphs. This is because when a graph may contain millions of nodes, even the storage of distances between all node pairs can become inefficient in practice. Therefore, it is desirable to design algorithms which can directly determine the significant changes in shortest path distances, without materializing the distances in individual snapshots. We present algorithms that are up to two orders of magnitude faster than such a solution, while retaining comparable accuracy.

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“…Therefore, this generic computation in three steps generates the centrality indices from Eqs. 4 and 5 in a total complexity of O n 3 .…”

Section: Definitionmentioning

confidence: 99%

“…Dynamic shortest paths more recently became very popular with the emergence of Intelligent or Dynamic Transportation Systems e.g. Chabini [7,8], Ahuja [3] or Demetrescu [11]. There are two well established approaches to this problem, which are quite different in essence.…”

Section: Dynamic Shortest Paths and Dynamic Indicesmentioning

confidence: 99%

Snapshot Centrality Indices in Dynamic FIFO Networks

2011

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The article introduces the concept of snapshot dynamic indices as centrality measures to analyse how the importance of nodes changes over time in dynamic networks. In particular, the dynamic stress-snapshot and dynamic betweenness snapshot are investigated. We present theoretical results on dynamic shortest paths in firstin first-out dynamic networks, and then introduce some algorithms for computing these indices in the discrete-time case. Finally, we present some experimental results exploring the algorithms' efficiency and illustrating the variation of the dynamic betweenness snapshot index for some sample dynamic networks.

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Dynamic Shortest Paths Minimizing Travel Times and Costs

Cited by 28 publications

References 12 publications

Solution approaches for determining user-oriented paths on dynamic networks

Solution approaches for determining user-oriented paths on dynamic networks

Finding Top-k Shortest Path Distance Changes in an Evolutionary Network

Snapshot Centrality Indices in Dynamic FIFO Networks

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